Why do Romeo and Juliet both think that Romeo's banishment is worse than death?

Romeo is banished from Verona by the Prince, at the risk of forfeiting his life if he should return. This is punishment for Romeo killing Tybalt, a Capulet, in a duel in vengeance for the death of his friend Mercutio, at Tybalt's hand.

When Juliet's nurse informs her about Romeo's sanction, she cries out in anguish:

That 'banished,' that one word 'banished,'
Hath slain ten thousand Tybalts. Tybalt's death
Was woe enough, if it had ended there:

... But with a rear-ward folloThat 'banished,' that one word 'banished,' Hath slain ten thousand Tybalts. Tybalt's death Was woe enough, if it had ended there:wing Tybalt's death,
'Romeo is banished,' to speak that word,
Is father, mother, Tybalt, Romeo, Juliet,
All slain, all dead. 'Romeo is banished!'
There is no end, no limit, measure, bound,
In that word's death; no words can that woe sound.

Juliet sees her lover's banishement as something worse than all sorrows put together and multiplied. She is overwrought by the thought and cannot contain herself. She feels that she is widowed and will die a maiden.

... die maiden-widowed.
Come, cords, come, nurse; I'll to my wedding-bed;
And death, not Romeo, take my maidenhead!

The cords which Romeo had procured so that he may gain entry to her bedroom have now become worthless, for Romeo will not be able to use them.

Romeo's response is similar to Juliet's. When friar Lawrence informs him of his banishment, he responds:

Ha, banishment! be merciful, say 'death;'
For exile hath more terror in his look,
Much more than death: do not say 'banishment.'

In similar vein he damns the punishement:

There is no world without Verona walls,
But purgatory, torture, hell itself.
Hence-banished is banish'd from the world,
And world's exile is death: then banished,
Is death mis-term'd: calling death banishment,
Thou cutt'st my head off with a golden axe,
And smilest upon the stroke that murders me.

Tis torture, and not mercy: heaven is here,
Where Juliet lives; and every cat and dog
And little mouse, every unworthy thing,
Live here in heaven and may look on her;
But Romeo may not: more validity,
More honourable state, more courtship lives
In carrion-flies than Romeo: they my seize
On the white wonder of dear Juliet's hand
And steal immortal blessing from her lips,
Who even in pure and vestal modesty,
Still blush, as thinking their own kisses sin;
But Romeo may not; he is banished:
Flies may do this, but I from this must fly:
They are free men, but I am banished.
And say'st thou yet that exile is not death?
Hadst thou no poison mix'd, no sharp-ground knife,
No sudden mean of death, though ne'er so mean,
But 'banished' to kill me?--'banished'?
O friar, the damned use that word in hell;
Howlings attend it: how hast thou the heart,
Being a divine, a ghostly confessor,
A sin-absolver, and my friend profess'd,
To mangle me with that word 'banished'?

Romeo is much more vociferous in his response to the word. He feels that it will be torture to be alive and without his love. He cannot bear the thought of not being able to see, touch, hear or kiss her when carrion flies can sit on her hand and 'steal immortal blessings from her lips. ' The thought of such a situation is much too painful for him to bear and he asks the friar not to even mention the word and hearing it will bring him further torment. It is better to be dead than in exile.

The two lovers' responses clearly indicate that they see Romeo's exile as more hurtful and damaging than anything and would rather prefer death. The reason for this is that they cannot bear the thought of knowing and loving one another and not being able to be together. In this regard, death would be a better option for they both would not exist and would thus not have to deal with the second to second torture for the rest of their lives of knowing about each other, but not being able to do anything about it.